Spatial Sensitivity to Absorption Changes for Various Near-Infrared Spectroscopy Methods: A Compendium Review

Abstract

This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media, particularly for measurements relevant to near-infrared spectroscopy. The three temporal domains, continuous-wave, frequency-domain, and time-domain, each obtain different optical data-types whose changes may be related to effective homogeneous changes in the absorption coefficient. Sensitivity is the relationship between a localized perturbation and the recovered effective homogeneous absorption change. Therefore, spatial sensitivity maps representing the perturbation location can be generated for the numerous optical data-types in the three temporal domains. The review first presents a history of the past 30 years of work investigating this sensitivity in optically diffuse media. These works are experimental and theoretical, presenting 1-, 2-, and 3-dimensional sensitivity maps for different near-infrared spectroscopy methods, domains, and data-types. Following this history, we present a compendium of sensitivity maps organized by temporal domain and then data-type. This compendium provides a valuable tool to compare the spatial sensitivity of various measurement methods and parameters in one document. Methods for one to generate these maps are provided in the appendix, including code. This historical review and comprehensive sensitivity map compendium provides a single source researchers may use to visualize, investigate, compare, and generate sensitivity to localized absorption change maps.

Figure 1:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 0.1 mm × 0.1 mm × 0.1 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Single-Distance (SD) Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=1.0\text{mm}$. (b) Iso-surface sliced at $S=3.000\times {10}^{-5}$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=0.0\text{mm}$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy (g): $0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 2:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Single-Distance (SD) Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=2.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$. (c) $x-z$ plane sliced at $=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=0.0\text{mm}$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 3:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Single-Distance (SD) Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $x-z$ plane sliced at $x=17.5\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 4:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Single-Distance (SD) Intensity $\left(I\right)$. (a)-(j) Different values of source-detector distance $\left(\rho \right)$. Generated using Diffusion Theory (DT). Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 5:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Single-Slope (SS) Intensity $\left(I\right)$.(a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=20.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 6:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Dual-Slope (DS) Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=30.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0,35.0,25.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 7:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Single-Slope (SS) Intensity $\left(I\right)$. (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 8:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Dual-Slope (DS) Intensity (I). (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 9:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Single-Slope (SS) Intensity $\left(I\right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 10:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Continuous-Wave (CW) Dual-Slope (DS) Intensity $\left(I\right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 11:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Distance (SD) Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=17.5\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 12:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Distance (SD) Intensity $\left(I\right)$. (a)-(j) Different values of modulation frequency $\left(f_{\mathit{\text{mod}}}\right)$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 13:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Distance (SD) phase of photon density waves $\left(\varphi \right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.010$ and $S=-0.005$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=17.5\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 14:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Distance (SD) phase of photon density waves $\left(\varphi \right)$. (a)-(j) Different values of source-detector distance $\left(\rho \right)$. Generated using Diffusion Theory (DT). Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 15:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Distance (SD) phase of photon density waves $\left(\varphi \right)$. (a)-(j) Different values of modulation frequency $\left(f_{\mathit{\text{mod}}}\right)$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 16:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Slope (SS) Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=20.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 17:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Dual-Slope (DS) Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=30.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0,35.0,25.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 18:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Slope (SS) Intensity $\left(I\right)$. (a)-(j) Different values of modulation frequency $\left(f_{\mathit{\text{mod}}}\right)$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 19:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Dual-Slope (DS) Intensity $\left(I\right)$. (a)-(j) Different values of modulation frequency $\left(f_{\mathit{\text{mod}}}\right)$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0,35.0,25.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 20:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Slope (SS) phase of photon density waves $\left(\varphi \right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=20.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 21:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Dual-Slope (DS) phase of photon density waves $\left(\varphi \right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=30.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0,35.0,25.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 22:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Slope (SS) phase of photon density waves $\left(\varphi \right)$. (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 23:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Dual-Slope (DS) phase of photon density waves $\left(\varphi \right)$. (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 24:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Slope (SS) phase of photon density waves $\left(\varphi \right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 25:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Dual-Slope (DS) phase of photon density waves $\left(\varphi \right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Modulation frequency $\left(f_{\mathit{\text{mod}}}\right):100\text{MHz}$

Figure 26:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Single-Slope (SS) phase of photon density waves $\left(\varphi \right)$. (a)-(j) Different values of modulation frequency $\left(f_{mod}\right)$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 27:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.1 mm measured by Frequency-Domain (FD) Dual-Slope (DS) phase of photon density waves $\left(\varphi \right)$. (a)-(j) Different values of modulation frequency $\left(f_{mod}\right)$. Generated using Diffusion Theory (DT). Source-detector distances $\left(\rho \text{s}\right):[25.0,35.0,35.0,25.0]\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 28:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 0.5 mm × 0.5 mm × 0.5 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=3.000\times {10}^{-5}$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=0.0\text{mm}$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 29:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=0.0\text{mm}$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 30:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.010$ and $S=-0.005$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=17.5\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 31:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a)-(j) Different values of source-detector distance $\left(\rho \right)$. Generated using Diffusion Theory (DT). Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 32:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a)-(i) Different values of mean time $\left(\bar{t}\right)$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gate: 500 ps Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 33:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a)-(j) Different values of mean time $\left(\bar{t}\right)$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gate: 500 ps

Figure 34:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a)-(i) Different values of time difference $\left(\Delta t\right)$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Mean time $\left(\bar{t}\right)$ gate: 1750 ps Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 35:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) gated Intensity $\left(I\right)$. (a)-(j) Different values of time difference $\left(\Delta t\right)$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Mean time $\left(\bar{t}\right)$ gate: 1750 ps

Figure 36:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) mean of the photon time-off-light distribution $(⟨t⟩)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.010$ and $S=-0.005$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=17.5\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 37:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 0.5 mm × 0.5 mm × 0.5 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=3.000\times {10}^{-5}$ and $S=-1.000\times {10}^{-5}$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=0.0\text{mm}$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Early time $\left(t\right)$ gate: [500, 1000] ps; Time $\left(t\right)$ gate: [1500, 2000] ps Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 38:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=0.0\text{mm}$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Early time $\left(t\right)$ gate: [500, 1000] ps; Time $\left(t\right)$ gate: [1500, 2000] ps Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 39:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.010$ and $S=-0.005$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=17.5\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Early time $\left(t\right)$ gate: [500, 1000] ps Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 40:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a)-(j) Different values of source-detector distance $\left(\rho \right)$. Generated using Diffusion Theory (DT). Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Early time $\left(t\right)$ gate: [500, 1000] ps Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 41:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a)-(e) Different values of average of gate center times $\left({\overline{\left(\bar{t}\right)}}_{\mathit{\text{gates}}}\right)$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gates: 500 ps Differance between gate center times $\left(\Delta (\bar{t}{)}_{\mathit{\text{gates}}}\right):1000\text{ps}$ Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 42:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a)-(j) Different values of average of gate center times $\left({\overline{\left(\bar{t}\right)}}_{\mathit{\text{gates}}}\right)$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gates: 500 ps Differance between gate center times $\left(\Delta (\bar{t}{)}_{\mathit{\text{gates}}}\right):1000\text{ps}$

Figure 43:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a)-(c) Different values of differance between gate center times $\left(\Delta (\bar{t}{)}_{\mathit{\text{gates}}}\right)$. Generated using Monte Carlo (MC). Source-detector distance $\left(\rho \right):0.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Scattering anisotropy $\left(g\right):0.9$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gates: 500 ps Average of gate center times $\left({\overline{\left(\bar{t}\right)}}_{\mathit{\text{gates}}}\right):1250\text{ps}$ Detector Numerical Aperature (NA): 0.5; Number of photons: 10⁹

Figure 44:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) difference in gated Intensity $\left(I\right)$. (a)-(i) Different values of differance between gate center times $\left(\Delta (\bar{t}{)}_{\mathit{\text{gates}}}\right)$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gates: 500 ps Average of gate center times $\left({\overline{\left(\bar{t}\right)}}_{\mathit{\text{gates}}}\right):1250\text{ps}$

Figure 45:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.010$ and $S=-0.005$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=17.5\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distance $\left(\rho \right):35.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 46:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Distance (SD) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$. (a)-(j) Different values of source-detector distance $\left(\rho \right)$. Generated using Diffusion Theory (DT). Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 47:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) gated Intensity $\left(I\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.040$ and $S=-0.015$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=20.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0] mm Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 48:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) gated Intensity $\left(I\right)$.(a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.040$ and $S=-0.015$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=30.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0, 35.0, 25.0] mm Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 49:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) gated Intensity $\left(I\right)$. (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 50:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) gated Intensity $\left(I\right)$. (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 51:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) gated Intensity $\left(I\right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 52:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) gated Intensity $\left(I\right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time $\left(t\right)$ gate: [1500, 2000] ps

Figure 53:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) gated Intensity $\left(I\right)$. (a)-(j) Different values of mean time $\left(\bar{t}\right)$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0] mm Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gate: 500 ps

Figure 54:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) gated Intensity $\left(I\right)$. (a)-(j) Different values of mean time $\left(\bar{t}\right)$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0, 35.0, 25.0] mm Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Time difference $\left(\Delta t\right)$ gate: 500 ps

Figure 55:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) gated Intensity $\left(I\right)$. (a)-(j) Different values of time difference $\left(\Delta t\right)$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0] mm Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Mean time $\left(\bar{t}\right)$ gate: 1750 ps

Figure 56:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) gated Intensity $\left(I\right)$. (a)-(j) Different values of time difference $\left(\Delta t\right)$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0, 35.0, 25.0] mm Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$ Mean time $\left(\bar{t}\right)$ gate: 1750 ps

Figure 57:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) mean of the photon time-of-flight distribution $(⟨t⟩)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=20.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0] mm Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 58:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) mean of the photon time-of-flight distribution $(⟨t⟩)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.020$ and $S=-0.010$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=30.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0, 35.0, 25.0] mm Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 59:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$. (a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.010$ and $S=-0.005$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=20.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0] mm Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 60:

Third angle projection of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$.(a) $x-y$ plane sliced at $z=10.0\text{mm}$. (b) Iso-surface sliced at $S=0.010$ and $S=-0.005$. (c) $x-z$ plane sliced at $y=0.0\text{mm}$. (d) $y-z$ plane sliced at $x=30.0\text{mm}$. Generated using Diffusion Theory (DT). Source-detector distances ($\rho$s): [25.0, 35.0, 35.0, 25.0] mm Index of refraction $\left(n\right)$ inside: 1.333 Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$ Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 61:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$. (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 62:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$. (a)-(h) Different values of mean source-detector distance $\left(\bar{\rho }\right)$. Generated using Diffusion Theory (DT). Difference in source-detector distance $\left(\Delta \rho \right):10.0\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 63:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Single-Slope (SS) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$

Figure 64:

$x-z$ plane of the Sensitivity to local absorption change $\left(𝒮\right)$ to a 10.0 mm × 10.0 mm × 2.0 mm perturbation scanned 0.5 mm measured by Time-Domain (TD) Dual-Slope (DS) variance of the photon time-of-flight distribution $\left({\sigma }^2\right)$. (a)-(i) Different values of difference in source-detector distance $\left(\Delta \rho \right)$. Generated using Diffusion Theory (DT). Mean source-detector distance $\left(\bar{\rho }\right):27.5\text{mm}$ Index of refraction $\left(n\right)$ inside: 1.333; Index of refraction $\left(n\right)$ outside: 1.000 Reduced scattering coefficient $\left({\mu }_s^{\prime }\right):1.10{\text{mm}}^{-1}$; Absorption coefficient $\left({\mu }_a\right):0.011{\text{mm}}^{-1}$